Dome-shaped patterned sapphire substrate with optimized curvature to enhance the efficacy of light emitting diodes

Abstract

This work has studied the influence of the generatrix's curvature of a dome-shaped patterned sapphire substrate (PSS) on the efficacy of GaN-based light emitting diodes (LEDs). The generatrix's central angle is carefully optimized by optical simulation. It is revealed that the dome-shaped PSS with a generatrix central angle of 10° is optimal to improve the luminous efficacy of LED devices. Subsequent crystal growth and characterization of LED wafers grown on dome-shaped PSSs with different generatrix central angles indicate that the central angle will not influence the as-grown LED wafers' crystalline quality, and the optimal central angle of 10° can enhance LED efficacy by about 19%.

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1. Introduction

Ever since high-efficiency p-GaN doping was successfully achieved by Akasaki,¹ GaN-based semiconductors have attracted intense interest due to wide applications for blue and white light emitting diodes (LEDs).^2–4 To date, LEDs' luminous efficiency has been much higher than that of filament lamps. However, to meet the market demand for high power lighting and make full use of LEDs' superiorities, luminous efficiency for LEDs still needs indispensable improvement. In general, luminous efficiency depends on both internal and external quantum efficiencies. Nowadays, the internal quantum efficiency of the best commercial LEDs has been up to 90%.⁵ However, the external quantum efficiency remains low, due to the total reflection in the interface between LED chips and the air.^6,7 In response to this problem, some approaches have been taken so far, such as deploying Bragg reflecting layer,⁸ photonic crystal and surface coarsening,^9,10 etc.,^11,12 which to some extent can enhance the external quantum efficiency. Of particular concern is the PSS technology,^13–15 which has been developed recently and can improve the external quantum efficiency on the premise of high-quality growth of LEDs' wafers. As the major influential elements for light path, parameters of patterns including their shape, dimension, and distribution for PSS play a significant role in LEDs' external quantum efficiency improvement.¹⁶ So far, several types of PSSs, such as hemisphere-shaped,^17–19 cone-shaped,²⁰ hexagon-shaped ones,^21,22 have been employed to enhance LEDs' luminous efficacy successfully.

It has been reported that cone-shaped PSS (CPSS) can relax stress of the wafer effectively,^23,24 and hence improve both IQE and EQE of LEDs simultaneously. Moreover, compared with the non-PSS case, CPSS-LEDs show larger enhancement in luminous efficacy. Such two mentioned aspects therefore verify the effectiveness of CPSS, and therefore make it the most commercially popular PSS. As mentioned, parameters of the pattern play an important role in the luminous efficacy of LEDs. When it comes to CPSSs, the generatrix of cone-shaped pattern is straight in general. However, if we turn the generatrix to curved, the cone-shaped pattern will change accordingly to so-called dome-shaped pattern, which changes the path of photons transmission and therefore the luminous efficacy of LEDs.

In this work, we study the influence of generatrix's curvature of dome-shaped PSS (DPSS) on the efficacy of LEDs via the 3D software, Solidworks, and the ray-tracing software, TracePro. The trends of luminous flux with regard to the generatrix's curvature are then revealed, and hereby the optimal DPSS for highly efficient GaN-based LEDs has been proposed. These results have been verified by the subsequent growth and characterizations of LED wafers on the DPSSs with various generatrix's curvatures.

2. Modeling

2.1. Pattern definition

The dome-shaped pattern in this work is derived from the cone-shaped pattern of PSS, by changing the curvature of the cone-shaped pattern's generatrix, as shown in Fig. 1a. The line (so-called L₃) represents the cone-shaped pattern's generatrix, and the curves (so-called L₁ and L₂) represent the dome-shaped patterns' generatrices. The dome-shaped pattern is described by four parameters as following, (1) diameter of the pattern, (2) height of the pattern, (3) distance between patterns, and (4) curvature of pattern's generatrix. For intuitive description, we actually use the central angle (so-called α in Fig. 1c) of the curve other than the curvature to represent the dome-shaped unit given a fixed diameter and height. In Fig. 1a, the central angle of L₁, L₂, L₃ is in descending, that is, the curvature of L₁, L₂, L₃ is in ascending. As for the cone-shaped pattern's generatrix, i.e., L₃, its central angle is 0°and the curvature becomes infinity.

Fig. 1 Description of the dome-shaped pattern and its parameters, (a) diameter, height, (b) distance, and (c) central angle α.

2.2. Model of LED chip

The simulation in this work includes the following steps, i.e., building the basic LED structure and patterns, defining the light source, tracing ray and collecting data. The first step of simulation is to build a 120 by 120 μm² model to represent a sapphire substrate. Via the drawing function integrated in Solidworks, dome-shaped pattern with given diameter, height, distance and central angle is accurately built on the substrate layer. We then use TracePro to build a 120 by 120 μm² unit to represent the LED chip, as shown in Fig. 2, and import the patterned sapphire substrate in it. The refractive index and thickness of each layer of the LED chip are detailed in Table 1. The mole fraction of indium in InGaN/GaN multiple quantum wells (MQWs), i.e., the active layer, is set as 15% in this work. To simplify the model, the absorption of light by materials and the effect from epitaxial defects are not taken into consideration during the simulation. In addition, the difference in refractive index between n-GaN and p-GaN caused by dopants is also neglected.^25,26

Fig. 2 Schematic structure of the LED chip model.

Table 1 Refractive index and thickness for each layer of the LED chip model

Simulation parameters	Sapphire	n-GaN	Active layer	p-GaN
Refractive index	1.67	2.45	2.45	2.45
Thickness (nm)	10^5	4 × 10^3	50	3 × 10^2

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The next step is to define the light source. We set the active layer's top and bottom planes as two planar lambertian sources and define the output power for each planar source as 5000 arbitrary units (arb. units). The total number of rays is set as 3000. Meanwhile, it is assumed that this LED model will not produce heat.

To collect emergent rays from each facet of the LED chip, we then build 6 virtual targets to collect the extracted lights from each facet. For each target, it has the same size as, and is 0.3 μm away from its corresponding facet of the LED chip. These targets can be regarded as 6 vacuum cubes which have neither material nor surface properties and will not cause any reflection. Analysis function in TracePro verifies that the luminous flux collected from these targets is exactly equal to that from the corresponding LED facet.

3. Simulation

To study the influence of the generatrix's central angle of dome-shaped pattern on LED's performance, we use the commercially popular CPSS as a reference whose diameter, height and distance are 2.0 μm, 1.5 μm and 3.0 μm, respectively. We then gradually increase the central angle of the dome-shaped unit from 0° to 90° with a step of 10°. For each step, simulation is run to collect the luminous flux from each facet of the LED chip.

4. Results and discussion of simulation

Fig. 3 is the simulation result. With the central angle increment, both the top and the bottom luminous flux change in the same tendency. When the angle increases in the range of 0–10°, they both present the slight increase of 100 a.u. and 61 a.u., respectively, and reach the maximum at 10° of the central angle. With the increase in the central angle, both the top and the bottom luminous flux decrease continuously, while the top luminous flux decreases faster than the bottom. It indicates that difference in the central angle affects more on the top facet of LED chips. On the contrary, as the central angle increases, the side luminous flux shows a different tendency. It decreases by 179 a.u. quickly in the range of 0–10°, and then increases slowly by 134 a.u. after 10°.

Fig. 3 Luminous flux from top, bottom and side facets of LED chips grown on DPSSs as a function of the central angle.

Fig. 4 shows the total luminous flux from the LED chips grown on DPSSs. As the angle increases, the total luminous flux declines in general. Detailed analysis reveals that the total flux decreases very slowly by 91.3 a.u. in the range from 0° to 40°, and decreases much more quickly by 405.8 a.u. when the angle is larger than 40°. The total luminous flux between 0–10° in the central angles keeps at a high and constant level. In other words, if we use 10° as the central angle, both the top and the bottom luminous flux from the DPSS-LED reach the maximum of 2191 a.u., 2474 a.u., respectively. At the same time, the total luminous flux also keeps a high value of 7448 a.u. at 10°. As we know, for the actual packaging process, LED chips are commonly packaged in surface mounted devices (SMD). In the SMD case, side luminous flux has little effect on LEDs' output efficiency. LEDs' output efficiency is mainly determined by the top luminous flux (flip-chip packaging), or the bottom luminous flux (dress-chip packaging) from the LED chips. We can hence deduce that the central angle of 10° for the DPSS is optimal to improve luminous efficacy of LED devices with SMD packaging.

Fig. 4 Total luminous flux from LED chips grown on DPSS as a function of the central angle.

For detailed study, more simulations around the generatrix's central angle of 10° with a step of 2° are carried out. The simulation results indicate that the trend of the luminous flux from LED chips agrees well with that mentioned above. DPSS-LED with 10° in the generatrix's central angle shows the maximal top and bottom luminous flux, and its total luminous flux keeps higher. Therefore, we can draw a conclusion that the optimal central angle for DPSS is 10°.

5. LED wafer fabrication

As pointed out, the DPSS with 10° in generatrix's central angle is optimal to obtain high light extraction yield for LEDs. Experiments have been carried out to verify the simulation result. For this purpose, we have fabricated two types of 2-inch PSS substrates. The first is of the DPSS with 10° in generatrix's central angle. The second is of the CPSS with 0° in generatrix's central angle. Both DPSS and CPSS share the same height of 1.55 μm and the same diameter of 2.55 μm.

Both DPSS and CPSS are fabricated by inductively coupled plasma (ICP) drying etching. Before etching, a uniform layer of photoresist is spread on the sapphire substrate by spin coating. The substrates are then carried out with ICP etching by following steps, i.e., exposure to ultraviolet light with photo mask, chemical corrosion and heat treatment. By controlling the etching time and the flux of the plasma gas, i.e., Cl₂/Ar, both the DPSS and CPSS with the specified parameters are fabricated on c-plane of sapphire substrates. To show patterns' shapes, a high-magnification LEO 1530 scanning electron microscope (SEM) is used for the cross-sectional SEM characterization.

Subsequently, GaN-based LED epitaxial wafers with the identical structure of Fig. 2 on both DPSS and CPSS are grown by metal organic chemical vapor deposition (MOCVD) under the same experimental conditions. During the growth, trimethylindium (TMIn), trimethylgallium (TMGa), and ammonia (NH₃) are used as the source materials of In, Ga, and N, respectively. Bicyclopentadienyl magnesium (Cp₂Mg) and silane (SiH₄) are used as the p-type and n-type doping sources, respectively. LED wafers consist of 2 μm thick u-GaN, 4.5 μm thick Si-doped n-GaN, 105 nm thick 7 pairs of InGaN/GaN (13/2 nm) MQWs with indium mole fraction of 15%, 20 nm thick layer of p-AlGaN electron blocking layer (EBL) and 200 nm thick Mg-doped p-GaN layers. GaN-based LED wafers on both DPSS and CPSS are evaluated by HRXRD (Bruker D8 X-ray diffractometer with Cu Kα1 X-ray source, λ = 1.5406 Å) for structural properties and by SEM (Nova Nano SEM 430 Holland) for morphology. A 405 nm laser (Y-Wafer GS4-GaN-R-405) is deployed as exciting source with an output power of 20 mW to study the optical properties of MQWs. The GAMMA Scientific GS-1190 RadoMA-Lite KEITHLEY 2400 system is used to evaluate electroluminescence (EL) properties of the LED wafers.

The cross-sections of DPSS and CPSS before epitaxial growth are shown in Fig. 5a and b, respectively. We can note that apart from the difference in the generatrix's curvature, the two samples share the identical diameter and height.

Fig. 5 The cross-sectional SEM images from (a) the DPSS and (b) CPSS.

Fig. 6 shows the XRD results of the LED wafers on both DPSS and CPSS. The full widths at half maximum (FWHM) for the X-ray rocking curve of (0002) LED wafers on DPSS (D-LED) and CPSS (C-LED) are 235 arcsec and 241 arcsec, respectively, and those of (101̄2) D-LED and C-LED are 236 arcsec and 230 arcsec, respectively. Evidently, the difference in FWHMs of LED wafers on the two samples is negligible. It means that the change in the generatrix's curvature of the dome-shaped PSS will cause little influence on the as-grown LED wafers' crystalline quality, which is good for the application of dome-shaped PSS in order to apply standard growth procedure.

Fig. 6 X-ray rocking curves for (a) the symmetric (0002) plane and (b) the asymmetric (101̄2) plane of D-LED and C-LED.

Fig. 7a represents the PL spectrum of the two LED wafers, i.e., D-LED and C-LED, respectively, which tells the quality of MQWs.²⁷ As can be seen, one PL spectrum resemble the other, in terms of either intensity or FWHM. The PL results evidently prove that the two PSSs have little influence on the as-grown MQWs' quality, which is consistent with the XRD results.

Fig. 7 (a) PL and (b) EL spectrum of MQWs grown on DPSS and CPSS.

The EL results from the two LED wafers are given in Fig. 7b. We have found that though the difference in FWHM is minuscule, the D-LED is of about 19% enhancement in the EL intensity when compared with the C-LED. This result straightforwardly verifies our simulation expectations that the dome-shaped PSS with 10° in generatrix's central angle is very effective to enhance LED efficacy.

6. Summary

In summary, a DPSS is derived from the commercially popular CPSS, and the influence from generatrix's curvature of the dome-shaped pattern has been carefully studied via the 3D software, Solidworks, and the ray-tracing software, TracePro. When the central angle of the dome-shaped pattern's generatrix is 10°, both the top and the bottom luminous flux from the DPSS-LED reach the maximum, and the total luminous flux also keeps a high value. The subsequent crystal growth proves that the change from CPSS to DPSS will not influence the as-grown LED wafers' crystalline quality, and the characterization of LED wafers reveals that the EL intensity of LED wafers on the optimal dome-shaped PSS can be increased by about 19%, which straight-forwardly proves the effectiveness of the optimized DPSS for improving LED efficacy.

Considering the current application of PSS, we foresee that the LED luminous efficacy can be further improved if this DPSS is applied instead of the commercially popular cone-shaped PSS.

Acknowledgements

This work is supported by National Science Fund for Excellent Young Scholars of China (Contract no. 51422203), National Science Foundation of China (Contract no. 51002052 and 51372001), Excellent Youth Foundation of Guangdong Scientific Committee (contract no. S2013050013882), Key Project in Science and Technology of Guangdong Province (Contract no. 2011A080801018), and Strategic Special Funds for LEDs of Guangdong Province (Contracts no. 2011A081301014, 2011A081301012 and 2012A080302002).

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